Universal spring mechanism for automobile suspension system design

ABSTRACT

A method for determining coil spring force line range corresponding to specific damper friction values using a universal spring mechanism and using the determined force line range in coil spring design. The method includes securing the mechanism to a suspension system including a damper, providing a controller for controlling actuator legs thereof for exerting force between upper and lower seats of the mechanism, and performing a capability study of the mechanism. The method further includes determining a desired coil spring force line position based upon the capability study, activating the mechanism to generate a desired coil spring force line based upon the desired coil spring force line position, performing damper friction measurements for determining a coil sp ring force line position for minimizing damper friction, determining the coil spring force line range based upon the damper friction measurements, and designing a coil spring based upon the coil spring force line range.

RELATED APPLICATIONS

This application claims benefit of priority of Provisional ApplicationSer. No. 60/514,896, filed Oct. 29, 2003, and further claims thepriority of parent application Ser. No. 10/817,981, filed Apr. 6, 2004,now U.S. Pat. No. 7,110,926.

BACKGROUND OF INVENTION

a. Field of Invention

The invention relates generally to suspension system design forautomobiles and the like, and, more particularly to a method andapparatus for finding a coil spring force line range which correspondsto specific damper friction values using a universal spring mechanism,and using the determined force line range in coil spring design methods.

b. Description of Related Art

Conventionally, a suspension coil spring force line positionspecification is determined from methods using Statics theories and/ormechanical simulation software such as ADAMS. These methods result in asingle ideal force line position for a simplified model. Since it isvirtually impossible to avoid manufacturing variability with regard toforce line position, the force line specification should preferably be arange that takes into account manufacturing variability, and not just anideal position. Furthermore, ideally the range would be determinedexperimentally, which would be more accurate than using simple Staticscalculations or simulations that require simplified models andassumptions. If the coil spring design needs to limit the damperfriction to a certain level from a riding comfort or durabilitystandpoint, an allowable spring force line position range needs to bedetermined by correlating actual damper friction to force line offsetand/or force line inclination. When using simulation software for thispurpose, results are invariably dependent on the friction coefficientused for the simulation. Moreover, today's suspension coil springdesigns require not only taking into account the one-dimensional forcealong the coil spring axis, but also require accounting for the exertionof a complex multi-dimensional force and torque field between the springseats.

Based upon the aforementioned factors and concerns, there remains a needfor a method and apparatus for finding a coil spring force line rangewhich is structurally and economically feasible to manufacture andutilize, and a system which efficiently and reliably determines a coilspring force line range for today's complex suspension coil springdesigns which are susceptible to one-dimensional forces along the coilspring axis as well as complex multi-dimensional force and torque fieldsbetween the spring seats.

SUMMARY OF INVENTION

The invention solves the problems and overcomes the drawbacks anddeficiencies of prior art suspension coil spring design systems byproviding a novel method and apparatus for finding a coil spring forceline range which corresponds to specific damper friction values using a6-degree-of-freedom (DOF) parallel mechanism, hereinafter referred to asa “universal spring mechanism,” and using the determined force linerange in coil spring design methods.

The present invention thus describes the design of the universal springmechanism which mimics the force and torque characteristics of a coilspring. This mechanism physically generates the 6-DOF force and torquefield of a coil spring, allowing for the experimental evaluation of thequasi-static force effects of a coil spring while at the design stage.Moreover, the universal spring mechanism according to the presentinvention may be readily used to investigate the relationship betweenspring characteristics and damper friction. The invention yet furtherdescribes a method for damper friction measurement by a newly developedtesting system including the universal spring mechanism.

The present invention thus provides a method for determining coil springforce line range corresponding to specific damper friction values usinga universal spring mechanism and using the determined force line rangein coil spring design. The method may include securing the universalspring mechanism to a suspension system including a damper, providing acontroller for controlling at least three actuator legs of the universalspring mechanism for exerting force between upper and lower seats of themechanism, and performing a capability study of the universal springmechanism. The method may further include determining a desired coilspring force line position based upon the capability study, activatingthe universal spring mechanism to generate a desired coil spring forceline based upon the desired coil spring force line position, performingdamper friction measurements for determining a coil spring force lineposition for minimizing damper friction, determining the coil springforce line range based upon the damper friction measurements, anddesigning a coil spring based upon the coil spring force line range.

For the method described above, the controller may be a controllerincluding an integrator element for reducing a steady state positionerror of a response of the universal spring mechanism to zero, aLead-Lag controller, and/or a controller including a Smith-predictor.Preferably, the controller may be a PI+Lead-Lag-controller with a SmithPredictor. For the method steps described above, the capability study ofthe universal spring mechanism may be performed such that a scannablecoil spring force line position range for a given spring is large enoughto cover a desired coil spring force line position range for a specificapplication. Moreover, performing the capability study may includecalculating a realizable coil spring force line by scanning forces andtorques generated by the universal spring mechanism, and adjustingmounting areas of at least one of the upper and lower seats if the coilspring force line position range is too large or too small. The methodmay further include computing a total force field based upon the desiredcoil spring force line position and dimensional configuration of theuniversal spring mechanism. For the method described above, performingthe damper friction measurements may include inputting an oscillation tothe suspension system, evaluating damper friction for a range of coilspring force line positions, and selecting an optimal coil spring forceline position or a range of coil spring force line positions forminimizing damper friction by sweeping upper and lower positions througha predetermined range.

The method may further include evaluating hysteresis in an output of aload cell mounted on the actuator leg to determine the damper friction.For the method described above, determining the coil spring force linerange may include evaluating a three-dimensional plot of damperfriction, and selecting a range of coil spring force line positionsbelow a predetermined acceptable damper friction. Alternatively,determining the coil spring force line range may include evaluating afriction contour map of damper friction, the map including informationregarding offset and inclination of the coil spring force line range,and selecting a range of coil spring force line positions below apredetermined acceptable damper friction. Yet further, determining thecoil spring force line range may include evaluating damper friction as afunction of offset and inclination of the coil spring force line range,and selecting a range of coil spring force line positions below apredetermined acceptable damper friction. For the method describedabove, the method may be used for experimental investigation of staticand dynamic characteristics of a coil spring.

The invention yet further provides a system for determining coil springforce line range corresponding to specific damper friction values usinga mechanism having spaced apart moveable platforms and a plurality ofactuable links interconnecting the platforms at corresponding joints onopposite ends of each link, and using the determined force line range incoil spring design. The system may include a structure for securing themechanism to a suspension system including a damper, a controller forcontrolling at least three of the links of the mechanism for exertingforce between upper and lower platforms of the mechanism, and a systemfor performing a capability study of the mechanism. The system fordetermining coil spring force line range may further include a systemfor determining a desired coil spring force line position based upon thecapability study, a system for performing damper friction measurementsfor determining a coil spring force line position for minimizing damperfriction, and a system for determining the coil spring force line rangebased upon the damper friction measurements.

For the system described above, the controller may be a controllerincluding an integrator element for reducing a steady state positionerror of a response of the universal spring mechanism to zero, aLead-Lag controller, and/or a controller including a Smith-predictor.The system for performing the damper friction measurements may include asystem for inputting an oscillation to the suspension system, a systemfor evaluating damper friction for a range of coil spring force linepositions, and a system for selecting an optimal coil spring force lineposition or a range of coil spring force line positions for minimizingdamper friction by sweeping upper and lower positions through apredetermined range. The system for determining coil spring force linerange may also include a load cell mounted on the links for determiningthe damper friction, a system for evaluating a three-dimensional plot ofdamper friction, and a system for selecting a range of coil spring forceline positions below a predetermined acceptable damper friction.Alternatively, the system for determining the coil spring force linerange may include a system for evaluating a friction contour map ofdamper friction, the map including information regarding offset andinclination of the coil spring force line range, and a system forselecting a range of coil spring force line positions below apredetermined acceptable damper friction. Yet further, the system fordetermining the coil spring force line range may include a system forevaluating damper friction as a function of offset and inclination ofthe coil spring force line range, and a system for selecting a range ofcoil spring force line positions below a predetermined acceptable damperfriction.

Additional features, advantages, and embodiments of the invention may beset forth or apparent from consideration of the following detaileddescription, drawings, and claims. Moreover, it is to be understood thatboth the foregoing summary of the invention and the following detaileddescription are exemplary and intended to provide further explanationwithout limiting the scope of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this specification, illustrate preferred embodiments of theinvention and together with the detail description serve to explain theprinciples of the invention. In the drawings:

FIG. 1( a) is a schematic diagram of a universal spring mechanismaccording to the present invention mounted on a strut;

FIG. 1( b) is a schematic diagram of the universal spring mechanism ofFIG. 1( a) illustrated in an installed configuration for damper frictionmeasurement for a MacPherson Strut type suspension system;

FIG. 1( c) is another simplified schematic diagram of the universalspring mechanism of FIG. 1( a) illustrated in an installed configurationfor damper friction measurement for a suspension system;

FIG. 1( d) is yet another simplified schematic diagram of the universalspring mechanism of FIG. 1( a) illustrated in an installed configurationfor damper friction measurement for a suspension system;

FIG. 2 is a flowchart illustrating an overview of the universal springscheme according to the present invention;

FIG. 3 shows schematic diagrams of the steps for inserting an extensiononto an actuator leg of the universal spring mechanism of FIG. 1( a);

FIGS. 4( a)-4(c) are schematic diagrams of parameter symbol definitionsaccording to the present invention;

FIG. 5 is a graph illustrating the typical step response of theuniversal spring mechanism described in FIG. 1( a);

FIG. 6 is a block diagram for a controller according to the presentinvention;

FIG. 7 is a graph illustrating an improved step response of theuniversal spring mechanism of FIG. 1( a);

FIG. 8( a)-8(b) show exemplary graphs of the realizable force lineposition for the upper and lower sides, respectively;

FIG. 9 is an exemplary graph of the realizable lower side force lineposition with the fixed upper force line position at the origin;

FIG. 10 is a graph illustrating the change in damper friction withvarious force line positions;

FIG. 11 is a graph illustrating three-dimensional visualization ofdamper friction according to the force line position;

FIG. 12 is a graph illustrating definition of force line offset andinclination;

FIG. 13 is a graph illustrating a friction contour map;

FIG. 14 is a graph illustrating the effect of force line offset andforce line inclination on damper friction; and

FIG. 15 is a graph illustrating typical load cell output during damperfriction, according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings wherein like reference numerals designatecorresponding parts throughout the several views, FIGS. 1-15 illustratecomponents and schematic diagrams related to a universal springmechanism according to the present invention, generally designated 30.

Universal spring mechanism 30 described in detail below has beensimilarly described in U.S. patent application Ser. No. 10/087,210,which is owned by the Assignee herein and the disclosure of which areincorporated herein by reference.

Referring to FIG. 1( a), the present invention describes universalspring mechanism 30 and a method of controlling mechanism 30 fordetermining the necessary force line range for a coil springexperimentally, without the requirement of making a prototype coilspring for a given application.

As shown in FIGS. 1( a) and 1(b), universal spring mechanism 30 may begenerally mounted on suspension system 32 instead of a coil spring.Mechanism 30 may generally include upper and lower seats 34, 36,respectively, and six actuator legs 38 disposed therebetween forapplying force for determining the necessary force line range for thecoil spring to be designed. Upper seat 34 may be operatively connectedto load cell 40 and damper 42, which may be further connected toassembly 44 including arms 46 and tire 48. Actuator legs 38 may includea normal height 60.

While the experimental setup for damper friction measurement for FIG. 1(b) illustrates the case of a MacPherson Strut type suspension, damperfriction measurement may be performed with either a full suspensionassembly, as shown in FIG. 1( b), or by simplified assemblies such asthe ones illustrated in FIGS. 1( c) and 1(d). For the simplifiedassemblies of FIGS. 1( c) and 1(d), tire 48 may be respectively replacedby a bearing 62 or fixture 64 for connection of damper 42 thereto. Itshould be noted that the experimental setups of FIGS. 1( b)-1(d) may beapplied to any type of suspension system in place of a coil spring, suchas coil-over shock applications for example.

Referring to FIGS. 1( a)-1(d), 2 and 3, the overview of the universalspring scheme is shown in FIG. 2. For FIGS. 1( a)-1(d), the set of 6-DOFforces between upper and lower seats 34, 36 of a McPherson suspensionsystem is generated by six actuator legs 38. Each actuator leg 38illustrated in FIGS. 2 and 3 may consist of a miniaturized custom madehydraulic cylinder 52, a load cell 54, and two ball joints 56.Kinematically, universal spring mechanism 30 requires 6-DOF, 3translational and 3 rotational. Ball joints 56 may be used to installactuators legs 38 to any inclined seats (i.e. upper and lower seats 34,36) to eliminate adverse moments on legs 38 and load cell 54. The use oftwo ball joints 56, instead of one ball joint and one universal joint,per leg 38 allows for an additional six degrees of freedom for theentire mechanism. These additional six degrees of freedom are present asthe non-constrained rotational motion of actuator legs 38 along eachcentral axis of hydraulic cylinder 52. These allowable rotations havevirtually no influence towards the generation of force between upper andlower seats 34, 36. For practical use of mechanism 30, the unconstrainedrotational motion of actuator legs 38 is beneficial in that it allowsarrangement of all six hydraulic hoses from each cylinder in anorganized manner.

As shown in FIG. 3, the length of each actuator leg 38 may be adjustedusing extension rods 58 installed between ball joints 56 and load cell54.

Referring to FIG. 2, the force of each actuator leg 38 may beindependently controlled by the closed-loop control scheme viacontroller 78 described in detail below. For the control scheme,generally, load cell 54 mounted on each actuator leg 38 may monitor theactual force acting along each leg 38. A voltage signal from load cell54 may be amplified, filtered, and sent to an A/D (Analog/Digital) board64 by signal coordinator 66. A voltage control signal may be determinedby the proposed closed-loop control scheme with the target leg forcecalculated from the desired force line position and flow to proportionalpressure valve driver 68 via a D/A (Digital/Analog) board 70. Thepressure of hydraulic cylinder 52 may be directly controlled byproportional pressure control valves (not shown).

Referring to FIG. 2, target force calculation 72 for each actuator leg38, based upon a desired force line position 74 and dimensionalconfiguration 76, will now be described in detail. The parameters usedbelow are defined in detail in reference to FIGS. 4( a)-4(c), for whichthe universal spring coordinate system is defined such that the centerof the upper mounting positions is set to origin, z-axis isperpendicular to the upper mounting seat 34, and x-axis is in the samedirection as the spring lower tip. From the desired force line position74 and dimensional configuration 76 for the system, the target force foreach leg 38 may be determined as follows.

Referring to FIGS. 4( a)-4(c), first, the unit vector of the i-th leg(u_(ix), u_(iy),u_(iz)) may be calculated under the universal springcoordinate system from Equation (1).

$\begin{matrix}{u_{i} = \frac{\left( {{x_{Ui} - x_{Li}},{y_{Ui} - y_{Li}},{z_{Ui} - z_{Li}}} \right)}{\sqrt{\left( {x_{Ui} - x_{Li}} \right)^{2} + \left( {y_{Ui} - y_{Li}} \right)^{2} + \left( {z_{Ui} - z_{Li}} \right)^{2}}}} & {{Equation}\mspace{14mu}(1)}\end{matrix}$

Total vertical force P_(z) may be given by the sum of the z-componentforce of the six legs.

$\begin{matrix}{P_{z} = {\sum\limits_{i = 1}^{6}{F_{i}u_{iz}}}} & {{Equation}\mspace{14mu}(2)}\end{matrix}$

The center of gravity on both seats 34, 36 may be approximated as theforce line position:

$\begin{matrix}{C_{Ux} = {{- \frac{1}{P_{z}}}{\sum\limits_{i = 1}^{6}{F_{i}u_{iz}{r_{Ui}}\cos\;\theta_{Ui}}}}} & {{Equation}\mspace{14mu}(3)} \\{C_{Uy} = {{- \frac{1}{P_{z}}}{\sum\limits_{i = 1}^{6}{F_{i}u_{iz}{r_{Ui}}\sin\;\theta_{Ui}}}}} & {{Equation}\mspace{14mu}(4)} \\{C_{Lx} = {{- \frac{1}{P_{z}}}{\sum\limits_{i = 1}^{6}{F_{i}u_{iz}{r_{Li}}\cos\;\theta_{Li}}}}} & {{Equation}\mspace{14mu}(5)} \\{C_{Ly} = {{- \frac{1}{P_{z}}}{\sum\limits_{i = 1}^{6}{F_{i}u_{iz}{r_{Li}}\sin\;\theta_{Li}}}}} & {{Equation}\mspace{14mu}(6)}\end{matrix}$

Since the moment about the force line axis does not influence the forceline position, it may be set to any value regardless if it can even berealized by an actual spring. The moment about the Z-axis (M_(z)) may beproduced mainly by the moment about the force line. Therefore, M_(z) mayalso be set to any value. For the present case, with M_(z) set to zero,the following equation results:

$\begin{matrix}{0 = {\sum\limits_{i = 1}^{6}{\left( {- 1} \right)^{i}F_{i}\sqrt{u_{ix}^{2} + u_{iy}^{2}}\cos\;\alpha_{i}}}} & {{Equation}\mspace{14mu}(7)} \\{{Where},{\alpha_{i} = \frac{{y_{Ui}u_{ix}} - {x_{Ui}u_{iy}}}{\sqrt{y_{Ui}^{2} + x_{Ui}^{2}} \cdot \sqrt{u_{ix}^{2} + u_{iy}^{2}}}}} & {{Equation}\mspace{14mu}(8)}\end{matrix}$

By solving Equations (2)-(7) as a system of linear equations for theunknowns F₁˜F₆, the target force for each leg may be readily determined.

The aforementioned closed-loop control scheme will now be described indetail.

Referring to FIGS. 2 and 5, in order to design controller 78, a stepresponse test may first be performed with universal spring mechanism 30modeled as discussed below. Specifically, in order to design controller78, a step response test may be performed individually on each actuatorleg 38 for identification of mechanism 30. FIG. 5 shows the typical stepresponse of universal spring mechanism 30 of FIGS. 1( a)-1(d). For FIG.5, characteristics including delay, nonlinearity, and time constant maybe attributable to factors such as the physical delay of the hydraulicvalve for hydraulic cylinder 52, ramp generator in the hydraulic drivercircuit (not shown), and signal conditioner of load cell 54. Because ofthe open loop control, steady state error may be observed due tofriction between the rod and cylinder. The characteristics of universalspring mechanism 30 in Laplace domain G^(h)(s) may be modeled as a delayand 1^(st) order system as follows to adapt to classical control theory.

$\begin{matrix}{{G(s)} = {e^{- {sL}_{h}} \cdot \frac{k_{h}}{1 + {sT}_{h}}}} & {{Equation}\mspace{14mu}(9)}\end{matrix}$

Where the subscript h represents a hydraulic system related parameter.From the actual step response result, the parameters L_(h), k_(h) andT_(h) may be estimated as 0.9, 0.67 and 0.4, respectively.

Based on the control system model discussed above, the following threecontroller design concepts may be implemented for controller 78according to the present invention.

For the first controller design, an integrator element is necessary tomake the system Type-1 so that the steady state position error reducesto zero. For the second controller design, a Lead-Lag controller may beapplied to improve system response by pole replacement. Alternatively,for the third controller design, a Smith-predictor may be applied toequivalently move the delay component out of the closed control loop.

By taking the aforementioned considerations into account, controller 78may preferably be a PI+Lead-Lag-Controller with a Smith Predictor. Ablock diagram for controller 78 is shown in FIG. 6, where, the subscriptc represents a controller related parameter, and T_(c2) is set to thesame value as T_(h) for pole replacement. The aforementioned controllerdesign provides improvement of the response for universal springmechanism 30, as discussed below.

Implementation of the aforementioned closed-loop control scheme will nowbe described in detail.

For implementation, the state variable equation in continuous timedomain for the proposed controller is expressed as follows:

$\begin{matrix}{\frac{\mathbb{d}x_{1}}{\mathbb{d}t} = {k_{c}\left( {u - x_{3}} \right)}} & {{Equation}\mspace{14mu}\left( {10a} \right)} \\{\frac{\mathbb{d}x_{2}}{\mathbb{d}t} = {{\frac{T_{1} - T_{2}}{T_{1}^{2}}x_{1}} - {\frac{1}{T_{1}}x_{2}}}} & {{Equation}\mspace{14mu}\left( {10b} \right)} \\{\frac{\mathbb{d}x_{3}}{\mathbb{d}t} = {{{- \frac{1}{T_{h}}}x_{3}} + {\frac{K_{h}}{T_{h}}\left( {1 - {\delta\left( {t - L} \right)}} \right)y}}} & {{Equation}\mspace{14mu}\left( {10c} \right)}\end{matrix}$

For implementation to Visual Basic code, the above-identified statevariable equation may be converted to discrete time domain as follows:

$\begin{matrix}{{x_{1}(n)} = {{k_{c}{\tau\left( {{u(n)} - {x_{3}(n)}} \right)}} + {x_{1}\left( {n - 1} \right)}}} & {{Equation}\mspace{14mu}\left( {11a} \right)} \\{{x_{2}(n)} = {\frac{1}{K_{1}}\left( {{\frac{T_{c1} - T_{c2}}{T_{c1}^{2}}{\tau \cdot {x_{1}(n)}}} + {x_{2}\left( {n - 1} \right)}} \right)}} & {{Equation}\mspace{14mu}\left( {11b} \right)} \\{{x_{3}(n)} = {\frac{1}{K_{2}}\left( {{\frac{k_{h}}{T_{h}}{\tau\left( {{y(n)} - {y\left( {n - \frac{L}{\tau}} \right)}} \right)}} + {x_{3}\left( {n - 1} \right)}} \right)}} & {{Equation}\mspace{14mu}\left( {11c} \right)} \\{{y(n)} = {{\frac{T_{c2}}{T_{c1}}{x_{1}(n)}} + {x_{2}(n)}}} & {{Equation}\mspace{14mu}\left( {11d} \right)} \\{{Where},{K_{1} = {1 + {\frac{1}{T_{h}}\tau}}},{K_{2} = {1 + {\frac{1}{T_{h}}\tau}}},} & \; \\{\tau = \text{Sampling~~Time.}} & \;\end{matrix}$

After implementation of controller 78, the step response is improved asshown in FIG. 7. For the response of FIG. 7, it can be seen thatalthough it takes longer for the output to settle, the output however iswell maintained by the controller to follow the target voltage, whichmeans that the corresponding force provided by each actuator leg 38 isalso well maintained.

In order to determine the force line range using universal springmechanism 30, the method according to the present invention may includethe following eleven steps.

The first step may include performing a capability study of universalspring mechanism 30 to ensure the scannable force line position rangefor a given spring is large enough to cover the desired force lineposition range for a subject application. For example, referring toFIGS. 8 and 9, based upon the specific geometric information ofuniversal spring mechanism 30 and vertical load specification providedby mechanism 30, the realizable force line range may be dynamicallycalculated by scanning the forces and torques generated by mechanism 30.FIG. 8 specifically shows an example of the realizable force lineposition for the upper side and the lower side (i.e. upper and lowerseats 34, 36), respectively. Likewise, referring to FIG. 9, by fixingeither the upper or lower force line positions to a specific value ofinterest, the realizable force line position of the other side can bedynamically calculated. FIG. 9 specifically shows an example of therealizable lower side force line position with the fixed upper forceline position being at the origin.

With universal spring mechanism 30 mounted on a strut as shown in FIG.1( a), each leg 38 may be installed between upper and lower seats 34,36, with the installed locations being measured by a coordinatemeasurement machine (CMM). Each actuator leg 38 may produce a force ofup to 3 KN for mechanism 30 illustrated for FIG. 1( a), which can beincreased based on the power of the hydraulic pump used. In the mountingcondition shown for FIG. 1( a), as discussed above, the adjustable forceline position range may be computed as shown in FIG. 8 where the upperside range is smaller than the lower side range due to the smallermounting area on the upper side. The implication of this fact is thatthe larger the spring seat, the larger the force line positionvariability becomes as the distribution of spring reaction force changessimilarly.

It should be noted that the force line position ranges shown in FIG. 8do not mean that the force line position can be adjusted to anycombination in the range, but that the force line position can bedistributed within that range under certain conditions. For example, ifthe upper position is fixed to (0,0), the adjustable range for the lowerposition is limited as shown in FIG. 9. Alternatively, if the range forforce line investigation requires a larger adjustable range, the lowermounting area must be enlarged using a lower seat adapter. Thus theadjustable range is dependent on the actuator mounting positions andtotal vertical force only, not the maximum force provided by each leg.

For the second step for force line range determination, an appropriatemounting seat adapter may be designed for universal spring mechanism 30to widen the scannable range if the aforementioned range is not wideenough. For example, if the aforementioned realizable force line rangeis not large enough, the mounting area of universal spring mechanism 30may be enlarged until the realizable force line range of the force lineis large enough to accommodate a specific application.

For the third step, as discussed earlier with reference to FIG. 3, thelength of universal spring mechanism 30 may be adjusted by inserting aproper extension adapter 58 to fit the workable range of mechanism 30 tothe spring height to be tested. If a height to be tested is longer thanan individual leg 38 of mechanism 30, an extension 58 of an appropriatelength may be used to correct the workable range of mechanism 30 to theheight to be tested.

Referring to FIG. 2, for the fourth step, a desired coil spring forceline position 74 may be determined.

For the fifth step, the corresponding total force field may be computedbased upon the desired force line position 74 and dimensionalconfiguration 76 of universal spring mechanism 30.

For the sixth step, universal spring mechanism 30 may be activated togenerate the desired coil spring force line.

For the seventh step, damper friction measurements (or other significantsuspension attribute measurements) may be performed by inputting aquasi-static oscillation with small stroke to suspension system 32 ofFIG. 1( b), for example. For damper friction measurement, the presentinvention uses a twin-tube type shock absorber with a separated typeMcPherson strut. Damper friction measurement may been performed underthe experimental setup shown in FIGS. 1( b)-1(d), where the force lineconnecting the center of upper seat 34 and bottom seat 36 is not on thedamper axis. The force line passes through the lower seat at (0, 18.5)in the aforementioned universal spring coordinate system. Therefore, itis expected that the damper friction would be minimized when the forceline is set to (0, 0) for the upper and (0, 18.5) for the lower seats34, 36, respectively. In order to find the optimal force line positionand/or the acceptable range to limit damper friction, the system of FIG.1( a) may be set in the actual vehicle mounting orientation. For thepresent invention, only the force lines on the Y-Z plane in theaforementioned universal spring coordinate system are discussed. Theupper and lower Y-positions of the force line (Uy, Ly) may be swept in arange from −20 mm to +20 mm with 10 mm increment and 5 mm increment,respectively. Referring next to FIG. 15, there is illustrated a typicalload cell output having hysteresis due to damper friction, for which theamount of the hysteresis corresponds to twice the friction force. Sinceuniversal spring mechanism 30 is always generating a consistent force,the load should not change during stroke. However, at the moment whenthe oscillating direction reverses, static friction in each leg 38causes a large load change due to the reaction speed of controller 78.Once the friction stabilizes, the controller maintains the force again,which does not create a problem if the friction is measured in steadystate.

For the eighth step, friction for damper 42 may be measured by readingthe amount of hysteresis in the output curve of load cell 54.

For the ninth step, steps 4-8 discussed above may be iterated withvarious force line positions.

Referring to FIG. 10, for the tenth step for force line rangedetermination, a friction map may be created according to the testedforce line positions and measured output. The results of the damperfriction measurement for damper 42 can be summarized as a plot shown inFIG. 10 for which each line corresponds to a different upper force lineposition (Uy) and how the damper friction changes when the lower forceline position (Ly) is scanned. The example of FIG. 10 only shows theresult when the force line is located on a certain vertical plane inFIGS. 1( a)-1(d). Alternatively, if the damper friction measurement isperformed on multiple vertical planes for testing the force line,multiple plots may be generated. For multiple vertical planes, the forceline position for minimizing the damper friction can be obtained fromplots such as FIG. 10, which illustrates the change in damper frictionwith various force line positions on the Y-Z plane.

For the eleventh step, a range of the force line position that limitsthe damper friction to a certain value may be determined. There are fourplot examples to find the force line position range corresponding to acertain damper friction range. From this experimental range, the coilspring force line position specification should be determined foroptimizing the coil spring design for vehicle targets and manufacturingability.

Based upon the eleven steps for force line range determination discussedabove, a first method for finding a force line range is by convertingthe plot of FIG. 10 to a 3D surface plot with surface interpolation asshown in FIG. 11, whereby the change in damper friction with respect tothe force line position becomes visually understandable. The range belowa specific constant friction plane (a horizontal plane bisecting thegraph in FIG. 11) corresponding to certain friction values would thus bethe acceptable force line range necessary to limit the damper frictionto that certain value.

For the first method for finding a force line range discussed above,force line offset and inclination are important factors at the coilspring design stage, and are defined in FIG. 12. For force line 80, theorigin of a coil spring coordinate system is at the center of upper seat34. The lower force line position is a projection up to the X-Y plane ofthe coil spring coordinate system. The distance between the upper forceline position and the lower force line position projection on the X-Yplane (shown as A in FIG. 12) is defined as the force line inclination.The distance to the center of the projected force line onto the X-Yplane from the origin (shown as B in FIG. 12) is defined as the offsetof the force line.

A second method for finding a force line range that limits the damperfriction to a certain value is to create a friction contour map as shownin FIG. 13. The plot for FIG. 13 can give additional numeric informationabout the force line range that limits the damper friction. The amountof offset and inclination of force line 80 can vary while limiting thedamper friction. From the friction contour map of FIG. 13, the followingmay be obtained. First, the friction at (Ly, Uy)=(18.5, 0) is theminimum as expected. This validates the system is working correctly.Secondly, if the force line passes through the upper position (0, 0),the lower position can be distributed in a range from approximately (0,5) to (0, 20) to limit the friction to 180N. Thirdly, if the force lineinclination is between −5 mm and −11 mm, the friction is consistent eventhough the force line offset ranges from −5 mm to 5 mm.

For a third method for finding a force line range, the plot of FIG. 13may be re-plotted by referring to the offset and inclination axes asshown in FIG. 14. From the plot of FIG. 14, the change in friction withrespect to spring force line offset and inclination is more obviouslyunderstandable. Force line offset may be defined as a distance betweenthe middle point of the force line projected onto the plane of upperseat 34 and the origin. Force line inclination may be defined as adistance between the upper and lower force line positions projected ontothe plane of upper seat 34. Therefore, spring side force is directlyrelated to the force line inclination. FIG. 14 further shows that thedamper friction depends on both inclination and offset. While there aremany combinations that may provide an acceptable level of damperfriction, the minimum friction is realized at only one location. If theresulting friction measurements were connected with a surface across alarge offset/inclination domain, as in FIG. 14, that surface could beanalogous to that of a boat hull as also shown in FIG. 14. The sideswould extend upward towards infinitely high friction as theoffset/inclination increases. The orientation in the inclination/offsetplane of the boat hull-like surface may be determined, not by itsrudder, but rather by the relative contribution of inclination versusoffset to cancel the applied moment on damper 42 from the suspensiongeometry. Using this surface, it is possible to select the optimum forceline inclination given a fixed offset condition. When designing aspring, if the spring offset is limited by space limitations ormanufacturing capability, an optimal spring inclination can still befound to satisfy the ultimate requirement. To summarize, it does notmake sense to only limit side force in order to control damper friction.Thus, the force line offset must also be taken into consideration. Itshould be noted that the resultant force line position is expressed inthe Universal coordinate system, which requires conversion to the springcoordinate system for spring design.

Yet a further fourth method for finding a force line range is similar tore-plotting FIGS. 11 and 13, whereby it is possible to create tofriction contour map based on FIG. 14 so that the allowable force lineoffset range and inclination range can be visually measured for springforce line design. From FIG. 14 and its contour map, the bestinclination to target can be found while being subjected to a limitedrealizable offset due to manufacturability and limited packagingconstraints.

The invention thus provides a 6-DOF programmable universal springmechanism 30 to mimic spring characteristics by applying a StewartPlatform type parallel mechanism. Mechanism 30 may be used toexperimentally find the ideal force line position and/or the range tolimit damper friction from the riding comfort standpoint without makingprototype springs, and can also be used to investigate any effects ofthe coil spring force line on vehicle self steering torque (SST). Theaforementioned capabilities of universal spring mechanism 30 can be usednot only to reduce coil spring design cycle time, but also to develop aspecific force line for a particular suspension instead of usingunrealistic, generalized force line bogeys. These design capabilitiescan compliment vehicle tuning to shorten and simplify the vehicle designprocess.

Although particular embodiments of the invention have been described indetail herein with reference to the accompanying drawings, it is to beunderstood that the invention is not limited to those particularembodiments, and that various changes and modifications may be effectedtherein by one skilled in the art without departing from the scope orspirit of the invention as defined in the appended claims.

1. A system for determining coil spring force line range correspondingto specific damper friction values using a force field generatormechanism to mimic a spring, said mechanism having spaced apart moveableplatforms and at least one actuable link interconnecting the platformsat corresponding joints on opposite ends of the link, the determinedforce line range being used in coil spring design, said systemcomprising: a structure for securing said mechanism to a suspensionsystem including a damper; a controller for controlling at least onelink of said mechanism for exerting force between upper and lowerplatforms of said mechanism; a system for performing a capability studyof said mechanism; a system for determining a desired coil spring forceline position based upon said capability study; a system for performingdamper friction measurements for determining a coil spring force lineposition for minimizing damper friction, wherein said system forperforming said damper friction measurements includes a system forinputting an oscillation to said suspension system, a system forevaluating damper friction for a range of coil spring force linepositions, and a system for selecting at least one of an optimal coilspring force line position and a range of coil spring force linepositions for minimizing damper friction by sweeping upper and lowerpositions through a predetermined range; a system for determining saidcoil spring force line range based upon said damper frictionmeasurements; a load cell mounted on said links for determining saiddamper friction; a system for evaluating a three-dimensional plot ofdamper friction; and a system for selecting a range of coil spring forceline positions below a predetermined acceptable damper friction.
 2. Thesystem for determining coil spring force line range according to claim1, wherein said system for determining said coil spring force line rangeincludes: a system for evaluating a friction contour map of damperfriction, said map including information regarding offset andinclination of said coil spring force line range; and a system forselecting a range of coil spring force line positions below apredetermined acceptable damper friction.
 3. The system for determiningcoil spring force line range according to claim 1, wherein said systemfor determining said coil spring force line range includes: a system forevaluating damper friction as a function of offset and inclination ofsaid coil spring force line range; and a system for selecting a range ofcoil spring force line positions below a predetermined acceptable damperfriction.